Shaft fitting system

ABSTRACT

A method of selecting a preferred golf shaft for a player who uses an existing golf shaft, according to one or more aspects of the present invention, may comprise gathering a plurality of empirical data sets, each data set corresponding to an individual golf shaft selected from a plurality of golf shafts; providing a plurality of specification codes, each associated with an individual empirical data set of the plurality of empirical data sets; from the plurality of specification codes, identifying a first specification code associated with the existing golf shaft; gathering feedback associated with the existing golf shaft from the player; and using the feedback to select, from the plurality of specification codes, a second specification code corresponding to the preferred golf shaft.

This is a Continuation of application Ser. No. 13/681,544, filed Nov.20, 2012, which is a Continuation of application Ser. No. 12/896,217filed Oct. 1, 2010 (now U.S. Pat. No. 8,337,217 B2 issued Dec. 25,2012), which claims the benefit of U.S. Provisional Application No.61/260,695 filed Nov. 12, 2009. The disclosure of the prior applicationsis hereby incorporated by reference herein in its entirety.

COPYRIGHT AUTHORIZATION

The disclosure below may be subject to copyright protection. Thecopyright owner has no objection to the facsimile reproduction by anyoneof the documents containing this disclosure, as they appear in thePatent and Trademark Office records, but otherwise reserves allapplicable copyrights.

BACKGROUND

It is well known in the art of golf-club making that the accuracy,trajectory, and distance of a golf shot are influenced by the flex orstiffness of a golf shaft. The bending stiffness of a golf shaft iscommonly represented in terms of a frequency, since bending stiffnessand vibration frequency are interrelated. Most manufacturers clamp theshaft only at the butt end to measure the vibration frequency. However,vibration frequency measurements, performed in this manner, do notaccurately represent the bending stiffness across the entire shaft.Alternatively, the bending stiffness of a golf shaft may be determinedby measuring the cantilever displacement of the golf shaft under a knownload. These measurements are typically taken only at the butt and tipsections of the shaft, thus providing limited bending stiffness data tothe golfer.

Additionally, the torsional stiffness of a golf shaft may be determinedby measuring the torsional displacement of the shaft under an appliedtorque for a given cantilever length. This method generates an overalltorsional stiffness value for the shaft, but does not provide thevarying localized torsional stiffness values across the shaft.Accordingly, it is difficult to fine tune the torsional stiffness of theshaft to fit the needs of the player.

SUMMARY

The present invention, in one or more aspects thereof, may comprise anadvantageous method of selecting a golf shaft that provides improvedplayer performance.

In one example, a method of selecting a preferred golf shaft for aplayer who uses an existing golf shaft, according to one or more aspectsof the present invention, may comprise gathering a plurality ofempirical data sets, each data set corresponding to an individual golfshaft selected from a plurality of golf shafts; providing a plurality ofspecification codes, each associated with an individual empirical dataset of the plurality of empirical data sets; from the plurality ofspecification codes, identifying a first specification code associatedwith the existing golf shaft; gathering feedback associated with theexisting golf shaft from the player; and using the feedback to select,from the plurality of specification codes, a second specification codecorresponding to the preferred golf shaft.

In another example, a method of selecting a preferred golf shaft for aplayer who uses an existing golf shaft, according to one or more aspectsof the present invention, may comprise generating a plurality of bendingstiffness profiles, each bending stiffness profile corresponding to anindividual golf shaft selected from a plurality of golf shafts;providing a plurality of specification codes, each associated with anindividual bending stiffness profile of the plurality of bendingstiffness profiles; from the plurality of specification codes,identifying a first specification code corresponding to the existinggolf shaft; gathering feedback associated with the existing golf shaftfrom the player; and using the feedback to select, from the plurality ofspecification codes, a second specification code corresponding to thepreferred golf shaft.

In yet another example, a method of selecting a preferred golf shaft fora player who uses an existing golf shaft, according to one or moreaspects of the present invention, may comprise generating a plurality oftorsional stiffness profiles, each bending stiffness profilecorresponding to an individual golf shaft selected from a plurality ofgolf shafts; providing a plurality of specification codes, eachassociated with an individual bending stiffness profile of the pluralityof torsional stiffness profiles; from the plurality of specificationcodes, identifying a first specification code corresponding to theexisting golf shaft; gathering feedback associated with the existinggolf shaft from the player; and using the feedback to select, from theplurality of specification codes, a second specification codecorresponding to the preferred golf shaft.

In yet another example, a method of selecting a preferred golf shaft fora player who uses an existing golf shaft, according to one or moreaspects of the present invention, may comprise gathering a plurality ofempirical data sets, each data set corresponding to an individual golfshaft selected from a plurality of golf shafts; providing a plurality ofspecification codes, each associated with an individual empirical dataset of the plurality of empirical data sets; from the plurality ofspecification codes, identifying a first specification codecorresponding to the existing golf shaft; gathering feedback associatedwith the existing golf shaft from the player; using the feedback toselect, from the plurality of specification codes, a secondspecification code corresponding to the preferred golf shaft; andsubstituting the existing golf shaft of the golf club with the preferredgolf shaft.

In yet another example, a method of selecting a preferred golf shaft fora player who uses an existing golf shaft, according to one or moreaspects of the present invention, may comprise gathering a plurality ofempirical data sets, each data set corresponding to an individual golfshaft selected from a plurality of golf shafts; storing the plurality ofempirical data sets in an electronic look-up table; performing acomputational analysis to standardize the empirical data for theplurality of golf shafts to produce a corresponding plurality ofspecification codes; from the plurality of specification codes,identifying a first specification code corresponding to the existinggolf shaft; gathering feedback associated with an existing golf shaftfrom the player; and using the feedback to select, from the plurality ofspecification codes, a second specification code corresponding to thepreferred golf shaft.

These and other features and advantages of the fitting method accordingto the invention in its various aspects, as provided by one or more ofthe examples described in detail below, will become apparent afterconsideration of the ensuing description, the accompanying drawings, andthe appended claims. The accompanying drawings are for illustrativepurposes only and are not intended to limit the scope of the presentinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary implementations of the present invention will now be describedwith reference to the accompanying drawings, wherein:

FIG. 1 is a perspective view of an exemplary golf club.

FIG. 2 is a plot of a plurality of shaft bending stiffness profiles.

FIG. 3 is a plot of a plurality of shaft torsional stiffness profiles.

FIG. 4 is a plot of bending stiffness profiles for a plurality of S-flexshafts.

FIG. 5 is a plot of bending stiffness profiles for a plurality of S-flexshafts.

FIGS. 6A and 6B illustrate a Pierce's Criterion R-value table.

FIG. 7 is a plot of bending stiffness data sets for a plurality ofS-flex shafts, according to one or more aspects of the presentinvention.

FIG. 8 is a plot of torsional stiffness data sets for a plurality ofS-flex shafts, according to one or more aspects of the presentinvention.

FIG. 9 is a plot of bending stiffness data sets for a plurality ofshafts, with each data set being vertically graduated into ten equalincrements.

FIG. 10 is a plot of bending stiffness data sets for a plurality ofshafts, with each data set being vertically graduated into ten equalincrements.

FIG. 11 is a plot of a bending stiffness profile for an exemplary shaft,according to one or more aspects of the present invention.

DESCRIPTION

In accordance with one or more aspects of the present invention, apreferred golf shaft may be selected for a player, who uses an existinggolf shaft, from a registry of commercially available golf shafts. Asshown in FIG. 1, each golf shaft 1 may include a butt end 2, generallyassociated with a grip 4 of a golf club 5, and a tip end 6, generallyassociated with a head 8 of a golf club 5. Moreover, each golf shaft maybe associated with a specification code, representative of a set ofempirical data relating to, e.g., a stiffness profile of the golf shaftor a frequency profile of the golf shaft. The specification code may beindicated by any type of indicating medium such as a color, mark,numeric, alphabetical, or alphanumeric indicia.

Manufacturers generally divide shafts into one of the following fivestiffness categories: senior flex (A-flex); regular flex (R-flex); stiffflex (S-flex); extra stiff flex (X-flex); or double extra stiff flex(XX-flex). Referring to FIGS. 2 and 3, the stiffness profile for eachshaft may be generated by measuring, e.g., the local stiffness inbending (FIG. 2) or the local stiffness in torsion (FIG. 3) at aplurality of points along the shaft. The localized stiffness in bending(EI) is defined as the product of the Young's modulus (E) and the momentof inertia (I) of the localized cross-sectional area of the shaft.Preferably, the bending stiffness profile, e.g., the bending stiffnessprofile 10, of each shaft is measured using, e.g., an automated EI curvetracer. The localized stiffness in torsion (GJ) is defined as theproduct of the Shear Modulus (G) and the polar moment of inertia (J).The torsional stiffness profile, e.g., the torsional stiffness profile12, may be measured using, e.g., an automated GJ curve tracer.

The stiffness profiles of each golf shaft may be converted into theappropriate specification code by using a formatting procedure.Initially, the stiffness profiles for all S-flex shafts are plotted onan x,y-coordinate plane wherein the x-axis represents the distance ofthe stiffness measurement from the butt end of the shaft and the y-axisrepresents the stiffness. Preferably, each of at least three verticallines passes through a distinct point on the x-axis. For example, asshown in FIGS. 4 and 5, a first vertical line 14 a may pass through afirst x-value (1), e.g., 0.25 m, which represents a point proximate thebutt end of the golf shaft, a second vertical line 14 b may pass througha second x-value (2), e.g., 0.50 m, a third vertical line 14 c may passthrough a third x-value (3), e.g., 0.75 m, and a fourth vertical line 14d may pass through a fourth x-value (4), e.g., 1.00 m, which representsa point proximate the tip end of the golf shaft. For each x-value (1),(2), (3), and (4), the intersection of the vertical line with eachS-flex stiffness profile delimits a set of S-flex data points, e.g.,S-flex data set 16, wherein each data point has a corresponding y-value.Each S-flex data set may include one or more outliers, i.e., one or moreS-flex data points that markedly deviate from other members of theS-flex data set. To eliminate the statistical outliers in each S-flexdata set, a percentage of the data points, e.g., 0.5%, 1%, 2%, or 5% ofthe data points, having the highest and lowest y-values, may beeliminated from consideration. Alternatively, Pierce's Criterion may beapplied to each S-flex data set to determine the statistically relevantmeasurements.

According to Pierce's Method, a measurement is considered a statisticaloutlier if the following relationship is satisfied:|x _(i) −x _(m) |>σR,where x_(i) is one of the measured data points in the S-flex data set,x_(m) is the mean of the S-flex data set, a is the standard deviation ofthe S-flex data set, and R is the ratio of the maximum allowabledeviation of an S-flex data point (x_(i)) from the mean (x_(m)) to thestandard deviation (σ). As shown in FIGS. 6A and 6B, the appropriate Rvalue depends on the sample size of an S-flex data set and the number ofsuspected outliers or “doubtful observations” to be rejected. Initially,it is assumed that one doubtful observation exists for an S-flex dataset. After selecting the appropriate R value for one doubtfulobservation, each data point of an S-flex data set is tested forstatistical relevance using Pierce's relationship, described above. Ifone data point of an S-flex data set is rejected, it is then assumedthat two doubtful observations exist in the data set. However, if morethan one data point of an S-flex data set is rejected for one doubtfulobservation, the next highest value of doubtful observations isselected. When testing each data point of an S-flex data set forstatistical relevance, assuming two or more doubtful observations, themean, the standard deviation, and the sample size retain the samevalues. After selecting the appropriate R value for two or more doubtfulobservations, the outliers are determined and eliminated using Pierce'srelationship. The remaining outliers are eliminated by sequentiallyincreasing the number of doubtful observations and following the sameprocedures, described above.

Once the outliers have been eliminated, the mean or average y-value isidentified for each S-flex data set at x-values (1), (2), (3), and (4).As shown in FIGS. 7 and 8, the average y-value, e.g., the averagey-values 18 a-d, for each S-flex data set may be designated with, e.g.,the numeric code 5, on the x,y-coordinate plane. Separate stiffnessplots may be generated for each remaining stiffness category, i.e.,A-flex, R-flex, X-flex, and XX-flex. For each stiffness plot, a data setmay be generated at each x-value (1), (2), (3), and (4) using theprocedure, described above, for determining the S-flex data sets. Theoutliers for each data set may be eliminated by using Pierce's Criterionor by eliminating a percentage of data points, also discussed above.After all outliers are eliminated for each stiffness plot, the remainingdata points of each data set are graphically aggregated on the S-flexstiffness plot.

As shown in FIGS. 9 and 10, the plot containing the data points from all5 stiffness categories is vertically graduated into ten equalincrements, each labeled with, e.g., a distinct numeric code thatsequentially increases from 0 to 9, at each x-value (1), (2), (3), and(4). The numeric code 0 substantially corresponds to the data pointhaving the lowest overall y-value in the aggregated data set, and thenumeric code 9 substantially corresponds to the data point having thegreatest overall y-value in the aggregated data set. As described above,the numeric code 5 corresponds to the average y-value for the S-flexdata set. Preferably, the numeric code 1 represents a stiffnessgenerally corresponding to that of an A-flex shaft, the numeric code 3represents a stiffness generally corresponding to that of an R-flexshaft, the numeric code 5 represents a stiffness generally correspondingto that of an S-flex shaft, the numeric code 7 represents a stiffnessgenerally corresponding to that of an X-flex shaft, and the numeric code9 represents a stiffness generally corresponding to that of a XX-flexshaft. Accordingly, each shaft may be converted into, e.g., a four digitnumerical code, representative of the shafts relative stiffness (y-axis)at x-values (1), (2), (3), and (4) on the x,y-coordinate plane. Forexample, a golf shaft having the stiffness profile shown in FIG. 11would have a specification code of 7536. Although the data point locatedat x-value (2) lies between the numeric codes 4 and 5, it is rounded tothe nearest whole integer of the code set to preserve simplicity.Preferably, each stiffness profile is analyzed by a computer softwareprogram, which converts each stiffness profile into a specification codeby automatically performing the code generating steps, described above.The specification code for each golf shaft model may be stored in ashaft registry, e.g., a printed chart or an electronic look-up table,and may be provided on the shaft.

Using the shaft registry, the specification code for the player'scurrent shaft model may be identified. Preferably, the specificationcode corresponding to the player's current shaft is used as a thresholdvalue in the process of selecting a preferred shaft having a new codeassociated therewith. To identify the new code, the threshold value maybe modified based on player feedback relating to his or her currentshaft's feel and performance. Player feedback may be gathered through ageneral feedback inquiry, e.g., an interview, a printed questionnaire,or an electronic interface. During the feedback inquiry, the player mayprovide general information about his or her current shot tendencies,e.g., average driver shot distance, swing speed, swing tempo, shotshape, and vertical ball flight/trajectory. A code adjustment value(CAV) may be assigned to each feedback response. For example, theplayer's average driver shot distance may be assigned one of a pluralityof available code adjustment values, each representative of a particulardistance range. More specifically, the player may be assigned one of thefollowing four code adjustment values depending on how far he or shedrives the ball: CAV 1111=<210 yards; CAV 3333=210 yards-240 yards; CAV5555=240 yards-270 yards; and CAV 7777=>270 yards.

The integers of each code adjustment value may be averaged together togenerate an average code adjustment value. If, for example, the codeadjustment value is identified as 5555, the average code adjustmentvalue would be 5, i.e., (5+5+5+5)/4. A similar method may be utilized togenerate an average threshold value. For example, if the threshold valueis 8866, the average threshold value would be 7, i.e., (8+8+6+6)/4.Accordingly, each integer of a threshold value may be decreased by thedifference between the average threshold value and the average codeadjustment value. Thus, if the average threshold value is 7 and theaverage code adjustment value is 5, each integer of a threshold value,e.g., 8866, would be decreased by a value of 2 for a final value ofe.g., 6644. Once the threshold value has been modified, the new valuemay represent either the new code or an intermediate value that may befurther modified.

Alternatively, the player's average swing speed, rather than the averagedriver shot distance, may be assigned one of a plurality of availablecode adjustment values, each representative of a particular swing speedrange. More specifically, the player may be assigned one of thefollowing four code adjustment values depending on how fast he or shecan swing the club head: CAV 1111=<85 m.p.h.; CAV 3333=85 m.p.h.-100m.p.h.; CAV 5555=100 m.p.h.-115 m.p.h.; and CAV 7777=>115 m.p.h. Asdescribed above, each integer of a threshold value may be decreased bythe difference between the average threshold value and the average codeadjustment value. Once the threshold value has been modified, the newvalue may represent either the new code or an intermediate value thatmay be further modified.

In another example, according to one or more aspects of the presentinvention, one or more integers of a threshold value (or an intermediatevalue, described above) may be modified based on the player's swingtempo. If, for example, the player's swing tempo comprises asubstantially constant angular acceleration, one or more integers of thethreshold value (or the intermediate value) may be increased by a valuebetween, e.g., about 1 and about 1.5. Alternatively, if the player'sswing tempo comprises a variable angular acceleration, one or moreintegers of the threshold value (or intermediate value) may be decreasedby a value between, e.g., about 1 and about 1.5. Once the thresholdvalue (or the intermediate value) has been modified, the new value mayrepresent either the new code or an intermediate value that may befurther modified.

In yet another example, according to one or more aspects of the presentinvention, one or more integers of a threshold value (or an intermediatevalue, described above) may be modified based on the player's desiredshot shape. If, for example, the player wants his or her shot to draw,the average threshold value (or the average intermediate value) may bereduced by a value between, e.g., about 1 and about 2. Alternatively oradditionally, the first integer of the threshold value (or theintermediate value) may be increased by a value between, e.g., about 1and about 2, and the final integer of the threshold value (or theintermediate value) may be decreased by a value between, e.g., about 1and about 2. If, instead, the player wants his or her shot to fade, theaverage threshold value (or the average intermediate value) may beincreased by a value between, e.g., about 1 and about 2. Alternativelyor additionally, the first integer of the threshold value (or theintermediate value) may be decreased by a value between, e.g., about 1and about 2, and the final integer of the threshold value (or theintermediate value) may be increased by a value between, e.g., about 1and about 2. Once the threshold value (or the intermediate value) hasbeen modified, the new value may represent either the new code or anintermediate value that may be further modified.

In yet another example, according to one or more aspects of the presentinvention, one or more integers of a threshold value (or an intermediatevalue, described above) may be modified based on the vertical ballflight and/or the trajectory of a player's shot. If, for example, thevertical ball flight, the launch angle, and/or the spin rate of the golfball are too high, the first integer of the threshold value (or theintermediate value) may be increased by a maximum value of, e.g., about2. If, however, the vertical ball flight, the launch angle, and/or thespin rate of the golf ball are too low, the last integer of thethreshold value (or the intermediate value) may be decreased by amaximum value of, e.g., about 2. Once the threshold value (orintermediate value) has been modified, the new value may representeither the new code or an intermediate value that may be furthermodified.

In yet another example, according to one or more aspects of the presentinvention, one or more integers of a threshold value (or an intermediatevalue) may be modified based on player feedback relating to the feel ofthe shaft during a golf swing. Accordingly, if the player describes theoverall stiffness of the shaft as too stiff, the average threshold value(or the average intermediate value) is decreased. Alternatively, if theplayer describes the overall stiffness of the shaft as too flexible, theaverage threshold value (or the average intermediate value) isdecreased. Once the threshold value or intermediate value has beenmodified, the new value may represent either the new code or anintermediate value that may be further modified.

After the new specification code is identified using player feedback,the player's current shaft may, e.g., be substituted with a preferredshaft having the new specification code associated therewith. In someinstances, the player's current shaft may be strategically cut at thetip and/or the butt such that the player's current shaft is convertedinto the preferred shaft having the new specification code associatedtherewith. The preferred shaft may be fabricated or ordered from anestablished supplier.

In the foregoing specification, the invention has been described withreference to specific exemplary aspects thereof. It will, however, beevident that various modifications and changes may be made theretowithout departing from the broader spirit and scope of the invention asset forth in the appended claims. The specification and drawings are,accordingly, to be regarded in an illustrative rather than a restrictivesense.

What is claimed is:
 1. A computer-implemented method for correlating a shaft with a specification code, the method comprising: receiving electronic data representing a measurement of shaft stiffness at each of at least three locations along the shaft; correlating a first portion of the shaft with a first unitless stiffness value and correlating a second portion of the shaft with a second unitless stiffness value, by converting the stiffness measurements into unitless values using a predetermined stiffness scale; associating the first and second unitless stiffness values with a specification code, the specification code representing a stiffness distribution of the shaft in an axial direction; and associating the specification code with the shaft.
 2. The method of claim 1, further comprising the step of storing the association of the specification code and the shaft.
 3. The method of claim 1, wherein each unitless stiffness value is an integer within a range of zero to nine.
 4. The method of claim 3, wherein the range of integers correspond to a range of stiffness such that a higher integer represents a higher stiffness.
 5. The method of claim 3, wherein an integer of one represents a stiffness generally corresponding to that of an A-flex shaft, an integer of three represents a stiffness generally corresponding to that of an R-flex shaft, an integer of five represents a stiffness generally corresponding to that of an S-flex shaft, an integer of seven represents a stiffness generally corresponding to that of an X-flex shaft, and an integer of nine represents a stiffness generally corresponding to that of an XX-flex shaft.
 6. The method of claim 1, wherein the shaft is a golf shaft.
 7. A method for determining a flex code of a shaft, the method comprising: measuring shaft stiffness at each of three locations along the shaft using a stiffness measuring device; correlating a first portion of the shaft with a first unitless stiffness value and correlating a second portion of the shaft with a second unitless stiffness value, by converting the stiffness measurements into unitless values using a predetermined stiffness scale; associating the first and second unitless stiffness values with a specification code the specification code representing a stiffness distribution of the shaft in an axial direction; and associating the specification code with the shaft.
 8. The method of claim 7, further comprising the step of storing the association of the specification code and the shaft.
 9. The method of claim 7, wherein each unitless stiffness value is an integer within a range of zero to nine.
 10. The method of claim 9, wherein the range of integers correspond to a range of stiffness such that a higher integer represents a higher stiffness.
 11. The method of claim 9, wherein an integer of one represents a stiffness generally corresponding to that of an A-flex shaft, an integer of three represents a stiffness generally corresponding to that of an R-flex shaft, an integer of five represents a stiffness generally corresponding to that of an S-flex shaft, an integer of seven represents a stiffness generally corresponding to that of an X-flex shaft, and an integer of nine represents a stiffness generally corresponding to that of an XX-flex shaft.
 12. The method of claim 7, wherein the shaft is a golf shaft. 